The Wigner bound, setting an upper limit on the scattering effective range,
is examined at different orders of contact effective field theory. Using
cutoff regulator we show that the bound loosens when higher orders of the
theory are considered.
For a sharp and a Gaussian regulators,
we conjecture an analytic
formula for the dependence of the Wigner bound on the theory's order.
It follows that the bound vanishes in the limit of infinite order.
Using a concrete numerical example we demonstrate that the above surmise
still holds after renormalization
at finite cutoff.
Studying the 3-body system with this example,
we have found that limiting the permissible range
of cutoffs by the Wigner bound, we avoid the
Thomas collapse, and don't need to promote the 3-body force to leading order.